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Search: id:A006010
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| A006010 |
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Number of paraffins (see Losanitsch reference for precise definition).
(Formerly M3897)
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+0
1
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| 1, 5, 20, 52, 117, 225, 400, 656, 1025, 1525, 2196, 3060, 4165, 5537, 7232, 9280, 11745, 14661, 18100, 22100, 26741, 32065, 38160, 45072, 52897, 61685, 71540, 82516, 94725, 108225, 123136, 139520, 157505, 177157, 198612, 221940, 247285
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjectures: If n is odd then a(n) = (1/8) * (n^4 + 2*n^3 + 2*n^2 + 2*n + 1) = Det(Transpose[M]*M) where M is the 2 X 3 matrix whose rows are [(n-1)/2, (n-1)/2], [(n-1)/2 + 1, 0] and [(n-1)/2 + 1, (n-1)/2 + 1]. If n is odd then a(n) = (1/8) * (n^4 + 2*n^3 + 2*n^2) = Det(Transpose[M]*M) where M is the 2x3 matrix whose rows are [n/2, 0], [n/2, n/2] and [n/2 + 1, 0]. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 30 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
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FORMULA
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Sum of [ 1, 3, 9... ](A005994)+[ 0, 0, 1, 3, 9, ... ]+2*[ 0, 1, 5, 15, 35... ](binomial(n, 4)).
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CROSSREFS
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Sequence in context: A006504 A007045 A102227 this_sequence A055383 A090133 A062988
Adjacent sequences: A006007 A006008 A006009 this_sequence A006011 A006012 A006013
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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